Rangers' administrators claimed Bill Miller could complete his purchase of the club by the end of the season after naming the American businessman as preferred bidder.
Miller succeeded with his £11.2million proposal, which involves buying the club's assets and moving them into a new company while trying to agree a deal with creditors to move the current company out of administration, after removing his conditions.
The vehicle recovery tycoon had previously sought assurances from the football authorities that his newco club would not be subjected to sanctions next season.
Completing his transaction before the Clydesdale Bank Premier League ends on May 13 would ensure that his request to acquire Rangers' share in the competition is subject to the discretion of the SPL board.
SPL clubs this week adjourned a vote on financial fair play proposals, which include financial and points penalties against newco clubs, until Monday, but the rules would not take effect until May 14 anyway.
Miller's success was announced in a statement from administrators Duff and Phelps, which read: "We are delighted to announce that today we have received an unconditional bid for the business and assets of Rangers Football Club plc from Mr Bill Miller which has been accepted and he is now the preferred bidder.
"Mr Miller now proposes to complete his transaction by the end of the season."
The administrators added that Miller's team had sought clarity in relation to potential footballing sanctions and the place of Rangers in the SPL.
"Significant progress has been made and discussions will continue throughout the period which Mr Miller now enjoys as preferred bidder," the statement read.
The SPL soon released a brief statement saying they would continue discussions with Miller and his team.
Miller's success comes at the expense of the partnership between the Blue Knights consortium and Sale Sharks owner Brian Kennedy, who aimed to take Rangers out of administration through a Company Voluntary Arrangement (CVA). Rangers' liabilities could rise to around £135million depending on the outcome of a tax tribunal held in January.
Joint-administrator Paul Clark said: "The barriers to a proposed stand-alone CVA are now too high.
"These barriers include, in particular, the absence of any bidder proposing unconditionally sufficient funds to enable a stand-alone CVA to take place.
"Crucially a stand-alone CVA would take so long now to effect, the club could not survive in administration.
"As a consequence, no party has been able to submit an unconditional bid in a stand-alone CVA scenario."
The Blue Knights bid was also conditional on acquiring Craig Whyte's 85% shareholding.
Clark said: "The bid from Mr Miller creates the most suitable framework to deal with the issue of the majority shareholding."
Rangers fans have previously protested against Miller's plans, arguing they could spell the end of the club formed in 1872.
But Clark claimed the club would continue and that Miller's bid preserves the history, although that appears dependent on a CVA being agreed at a later date.
"There is no liquidation involved in this strategy and we cannot stress that strongly enough," he said.
"As we stated at the outset, one of the prime objectives of the administration was to achieve a CVA which would deliver a return to creditors. Mr Miller's bid meets this criteria."
Clark added: "Mr Miller's proposal involves the use of a specially created newco in addition to the retention of the Rangers Football Club plc.
"The business and assets he proposes to purchase will be sheltered in a newco and returned to the plc once the plc has been 'cleaned up'.
"He sees this route as a necessity rather than a choice and in our view this is an entirely workable strategy.
"Indeed to ensure the continuing operation of the club beyond the end of May it is in our view a very compelling strategy."
Clark added: "The bid submitted by Mr Miller is substantially greater than any other proposal and provides the best return to creditors, a fundamental part of our duties as administrators."
As well as potential difficulties in agreeing a CVA with creditors such as Her Majesty's Revenue and Customs and investment firm Ticketus, Miller has other obstacles in rebuilding the club.
PFA Scotland chief executive Fraser Wishart has warned that players would not be obliged to move to a newco club and could leave Ibrox for free.
Rangers have been hit with a 12-month embargo on signing players aged over 17, a decision which will be subject to a Scottish Football Association appeal.
UEFA also has rules stating that a club must be a member of a national association for three years before being allowed entry to European competition.
Rangers will not play in Europe next season after failing to meet financial criteria needed for a UEFA licence.
The SFA will seek talks with the American.
A statement read: "It is our intention to enter into detailed discussions with Mr Miller to clarify his position and to establish his strategy to ensure a sustainable future for the club.
"We will make further comment when that process has been completed."
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